(Hard) is not hard, it's casual content. You can queue for it without knowing anything about it.

(Extreme) and Minstrel's Ballad is considered high-end content. It typically removes the orange telegraphs, has faster cast times, increased damage and new mechanics. It can take hours or days of progression even when you've watched a guide. If you queue for them, it only finds people from Mentor Roulette (a minority of veteran players queue for this chasing a mount) as well as those who queue directly for the duty. It syncs to a higher item level than when it released and you get a buff called the Echo when you die to make it easier, but some of them can still be challenging with this.

Most people clear them by recruiting in Party Finder for a level 90 to kill it in a few hits using the Unrestricted setting, which prevents them from being synced down from level 90 to level 50. The consequence of that is you don't experience the challenge of it, but there are not very many people who are interested in old challenging content. They mostly just do the newest challenging content. To do old challenging content it can help to find 7 people who also want to do this regularly at the times you are available.

(Savage) and Coil Turns are high-end content, regarded as harder and more punishing than extremes but that's not completely strict (some extremes can be harder than some savage bosses). Extremes are partly easier because they are meant to be farmed hundreds of times for a mount whereas Savage is only meant to be cleared once a week so it's alright if you aren't as consistent at it.

(Ultimate) is what you can do once you clear savage. It's not expected that very many people will do ultimates and the only rewards are a shiny weapon, a title and an extra materia slot so that nobody feels pressured to do them for gear. They are designed to be streamed and watched instead of you doing them yourself.